correct ordered factor definition (#1686)

Co-authored-by: Hadley Wickham <h.wickham@gmail.com>

factors.qmd

@@ -56,7 +56,7 @@ To create a factor you must start by creating a list of the valid **levels**:
 
 ```{r}
 month_levels <- c(
-  "Jan", "Feb", "Mar", "Apr", "May", "Jun", 
+  "Jan", "Feb", "Mar", "Apr", "May", "Jun",
   "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"
 )
 ```
@@ -169,7 +169,7 @@ relig_summary <- gss_cat |>
     n = n()
   )
 
-ggplot(relig_summary, aes(x = tvhours, y = relig)) + 
+ggplot(relig_summary, aes(x = tvhours, y = relig)) +
   geom_point()
 ```
 
@@ -212,7 +212,7 @@ What if we create a similar plot looking at how average age varies across report
 #| fig-alt: |
 #|   A scatterplot with age on the x-axis and income on the y-axis. Income
 #|   has been reordered in order of average age which doesn't make much
-#|   sense. One section of the y-axis goes from $6000-6999, then <$1000, 
+#|   sense. One section of the y-axis goes from $6000-6999, then <$1000,
 #|   then $8000-9999.
 rincome_summary <- gss_cat |>
   group_by(rincome) |>
@@ -221,7 +221,7 @@ rincome_summary <- gss_cat |>
     n = n()
   )
 
-ggplot(rincome_summary, aes(x = age, y = fct_reorder(rincome, age))) + 
+ggplot(rincome_summary, aes(x = age, y = fct_reorder(rincome, age))) +
   geom_point()
 ```
 
@@ -257,29 +257,29 @@ This makes the plot easier to read because the colors of the line at the far rig
 #|     A line plot with age on the x-axis and proportion on the y-axis.
 #|     There is one line for each category of marital status: no answer,
 #|     never married, separated, divorced, widowed, and married. It is
-#|     a little hard to read the plot because the order of the legend is 
-#|     unrelated to the lines on the plot. Rearranging the legend makes 
-#|     the plot easier to read because the legend colors now match the 
-#|     order of the lines on the far right of the plot. You can see some 
-#|     unsurprising patterns: the proportion never married decreases with 
-#|     age, married forms an upside down U shape, and widowed starts off 
+#|     a little hard to read the plot because the order of the legend is
+#|     unrelated to the lines on the plot. Rearranging the legend makes
+#|     the plot easier to read because the legend colors now match the
+#|     order of the lines on the far right of the plot. You can see some
+#|     unsurprising patterns: the proportion never married decreases with
+#|     age, married forms an upside down U shape, and widowed starts off
 #|     low but increases steeply after age 60.
 by_age <- gss_cat |>
-  filter(!is.na(age)) |> 
+  filter(!is.na(age)) |>
   count(age, marital) |>
   group_by(age) |>
   mutate(
     prop = n / sum(n)
   )
 
 ggplot(by_age, aes(x = age, y = prop, color = marital)) +
-  geom_line(linewidth = 1) + 
+  geom_line(linewidth = 1) +
   scale_color_brewer(palette = "Set1")
 
 ggplot(by_age, aes(x = age, y = prop, color = fct_reorder2(marital, age, prop))) +
   geom_line(linewidth = 1) +
-  scale_color_brewer(palette = "Set1") + 
-  labs(color = "marital") 
+  scale_color_brewer(palette = "Set1") +
+  labs(color = "marital")
 ```
 
 Finally, for bar plots, you can use `fct_infreq()` to order levels in decreasing frequency: this is the simplest type of reordering because it doesn't need any extra variables.
@@ -288,7 +288,7 @@ Combine it with `fct_rev()` if you want them in increasing frequency so that in
 ```{r}
 #| fig-alt: |
 #|   A bar char of marital status ordered from least to most common:
-#|   no answer (~0), separated (~1,000), widowed (~2,000), divorced 
+#|   no answer (~0), separated (~1,000), widowed (~2,000), divorced
 #|   (~3,000), never married (~5,000), married (~10,000).
 gss_cat |>
   mutate(marital = marital |> fct_infreq() |> fct_rev()) |>
@@ -409,21 +409,24 @@ Read the documentation to learn about `fct_lump_min()` and `fct_lump_prop()` whi
 
 ## Ordered factors {#sec-ordered-factors}
 
-Before we go on, there's a special type of factor that needs to be mentioned briefly: ordered factors.
-Ordered factors, created with `ordered()`, imply a strict ordering and equal distance between levels: the first level is "less than" the second level by the same amount that the second level is "less than" the third level, and so on.
-You can recognize them when printing because they use `<` between the factor levels:
+Before we continue, it's important to briefly mention a special type of factor: ordered factors.
+Created with the `ordered()` function, ordered factors imply a strict ordering between levels, but don't specify anything about the magnitude of the differences between the levels.
+You use ordered factors when you know there the levels are ranked, but there's no precise numerical ranking.
+
+You can identify an ordered factor when its printed because it uses `<` symbols between the factor levels:
 
 ```{r}
 ordered(c("a", "b", "c"))
 ```
-
-In practice, `ordered()` factors behave very similarly to regular factors.
+In both base R and the tidyverse, ordered factors behave very similarly to regular factors.
 There are only two places where you might notice different behavior:
 
 -   If you map an ordered factor to color or fill in ggplot2, it will default to `scale_color_viridis()`/`scale_fill_viridis()`, a color scale that implies a ranking.
--   If you use an ordered function in a linear model, it will use "polygonal contrasts". These are mildly useful, but you are unlikely to have heard of them unless you have a PhD in Statistics, and even then you probably don't routinely interpret them. If you want to learn more, we recommend `vignette("contrasts", package = "faux")` by Lisa DeBruine.
+-   If you use an ordered predictor in a linear model, it will use "polynomial contrasts". These are mildly useful, but you are unlikely to have heard of them unless you have a PhD in Statistics, and even then you probably don't routinely interpret them. If you want to learn more, we recommend `vignette("contrasts", package = "faux")` by Lisa DeBruine.
 
-Given the arguable utility of these differences, we don't generally recommend using ordered factors.
+For the purposes of this book, correctly distinguishing between regular and ordered factors is not particularly important.
+More broadly, however, certain fields (particularly the social sciences) do use ordered factors extensively.
+In these contexts, it's important to correctly identify them so that other analysis packages can offer the appropriate behavior.
 
 ## Summary